bec If the available thermal energy is not much bigger than this energy gap kBT ≲ △ε, KE = 3/2 kT (or kBT) (kB: boltzmann constant)

Einstein's Physics: Atoms, Quanta, and Relativity - ...

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Ta-Pei Cheng - 2013 - ‎Science

If the available thermal energy is not much bigger than this energy gap kBT ≲ △ε, ... On the other hand, Bose–Einstein condensation (BEC) is the phenomenon ..

 KE = 3/2 kT (or kBT) (kB: boltzmann constant)

kT is the product of the Boltzmann constant, k, and the temperature, T. This product is used in physics as a scaling factor for energy values in molecular-scale systems (sometimes it is used as a unit of energy), as the rates and frequencies of many processes and phenomena depend not on their energy alone, but on the ratio of that energy andkT, that is, on E / kT (see Arrhenius equation, Boltzmann factor). For a system in equilibrium in canonical ensemble, the probability of the system being in state with energy E is proportional to e^{−ΔE / kT}. More fundamentally, kT is the amount of heat required to increase the thermodynamic entropy of a system, in natural units, by one nat.

In macroscopic scale systems, with large numbers of molecules, RT value is commonly used; its SI units are joules per mole (J/mol): (RT = kT ⋅ N_A).

In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution^[1]) is a probability distribution, probability measure, or frequency distribution of particles in a system over various possible states. The distribution is expressed in the form

where  is state energy (which varies from state to state), and